Dove hatching advice, please

While feeding the birds this morning I discovered one of my doves sitting on an egg. I have had these doves not even a year yet so I am still learning the ropes. In January she hatched out a baby and the next day it fell out of the nest and froze. Its only in the 20's right now so I don't know if I should let her sit on the nest in their coop, then take the baby after it has hatched, move her and the nest inside the house, or take the egg and incubate it.

Any advice or suggestions is greatly appreciated. The doves are in a big coop with quail and pigeons.